Answered: Can you help me solve this using R?…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 13PPS

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Can you help me solve this using R?

10.1) The experimental data below contains food intake (in Kcal) for 15 men on the day following two nights of only 4 hours of sleep each night and for 15 mean on the day following two nights of 8 hours of sleep each each night. The mean participating in this experiment were randomly assigned to one of the two sleep conditions.

four.hr.grp <- c(3585, 4470, 3068, 5338, 2221, 4791, 4435, 3099, 3187, 3901, 3868, 3869, 4878, 3632, 4518)
eight.hr.grp <- c(4965, 3918, 1987, 4993, 5220, 3653, 3510, 3338, 4100, 5792, 4547, 3319, 4304, 4057)

i) Compute the mean and standard deviation of the two groups. Comment on what you see.
ii) Create a boxplot and histogram (with a fitted normal density curve) for the food intake in the two groups. Is the normal distribution a reasonable assumption for the sodium intake in both classes?
iii) Carry out a two-sample t test with alpha = 0.05 to determine if there is a significant difference in mean food intake for the two different sleep conditions.
iv) State the results of your t-test. Can you make conclusive statement based on the information in your data? Why?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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